Techniques and apparatus for generalized trisoup geometry coding

ABSTRACT

There is included a method and apparatus comprising computer code configured to cause a processor or processors to perform obtaining a leaf node of geometry based point cloud compression (G-PCC) data, splitting the leaf node into a plurality of cuboids, deriving separate triangle soups for each of the cuboids, and coding a plurality of flags respectively for each of the edges of each of the cuboids, where the plurality of flags indicate whether vertices of the separate triangle soups are present on ones of the edges.

CROSS REFERENCE TO RELATED APPLICATION

The present application is a continuation of U.S. application Ser. No.17/004,616, filed Aug. 27, 2020, claims priority to provisionalapplication U.S. 62/895,339 filed on Sep. 3, 2019 which is herebyexpressly incorporated by reference, in its entirety, into the presentapplication.

BACKGROUND 1. Field

The present disclosure is directed to point cloud coding technologiesmore specifically to point cloud geometry compression includinggeneralizing the Trisoup lossy compression of MPEG/G-PCC and including afast RDO scheme.

2. Description of Related Art

Advanced 3D representations of the world are enabling more immersiveforms of interaction and communication. They also allow machines tounderstand, interpret and navigate our world. Point clouds have beenwidely used as a 3D representation of the world. Several use casesassociated with point cloud data have been identified, and correspondingrequirements for point cloud representation and compression have beendeveloped.

A point cloud is a set of points in a 3D space, each with associatedattributes, e.g. color, material properties, etc. Point clouds can beused to reconstruct an object or a scene as a composition of suchpoints. They can be captured using multiple cameras and depth sensors invarious setups and may be made up of thousands up to billions of pointsin order to realistically represent reconstructed scenes.

Compression technologies are needed to reduce the amount of datarequired to represent a point cloud. As such, technologies are neededfor lossy compression of point clouds for use in real-timecommunications and six Degrees of Freedom (6 DoF) virtual reality. Inaddition, technology is sought for lossless point cloud compression inthe context of dynamic mapping for autonomous driving and culturalheritage applications, etc. MPEG has started working on a standard toaddress compression of geometry and attributes such as colors andreflectance, scalable/progressive coding, coding of sequences of pointclouds captured over time, and random access to subsets of the pointcloud.

In lossy G-PCC Trisoup geometry coding, it may happen that a manifold,for example, is too complicated to model using a limited number of freeparameters.

Therefore, there is a desire for a technical solution to such problems.

SUMMARY

To address one or more different technical problems, this disclosuregeneralizes the Trisoup technology adopted in the MPEG/G-PCC to tacklethis problem, and a rate-distortion optimization (RDO) scheme is alsoanticipated for the proposed generalized Trisoup.

There is included a method and apparatus comprising memory configured tostore computer program code and a processor or processors configured toaccess the computer program code and operate as instructed by thecomputer program code. The computer program code includes obtaining codeconfigured to cause the at least one processor to obtain a leaf node ofgeometry based point cloud compression (G-PCC) data, splitting codeconfigured to cause the at least one processor to split the leaf nodeinto a plurality of cuboids, deriving code configured to cause the atleast one processor to derive separate triangle soups for each of thecuboids, and coding code configured to cause the at least one processorto code a plurality of flags respectively for each of the edges of eachof the cuboids, where the plurality of flags indicate whether verticesof the separate triangle soups are present on ones of the edges.

According to exemplary embodiments, the coding code is furtherconfigured to cause the at least one processor to entropy code asignaling of a splitting pattern of the leaf node by two bits, and thetwo bits indicate whether the leaf node is split into the cuboids inhalf along one of an x-axis, a y-axis, and a z-axis.

According to exemplary embodiments, a location, at which the leaf nodeis split and along at least one of the x-axis and the y-axis is signaledfor each of the cuboids.

According to exemplary embodiments, the deriving code is furtherconfigured to cause the at least one processor to derive the trianglesoups recursively at the leaf node among a plurality of lead nodes ofthe G-PCC data.

According to exemplary embodiments, the coding code is furtherconfigured to cause the at least one processor to entropy code asignaling of a splitting pattern of the leaf node by three bits, and thethree bits indicate whether the leaf node is split into the cuboids inhalf along one of an x-axis, a y-axis, a z-axis, a combination of thex-axis and the y-axis, a combination of the x-axis and the z-axis, acombination of the y-axis and the z-axis, and a combination of thex-axis, the y-axis, and the z-axis.

According to exemplary embodiments, the location, at which the leaf nodeis split and along at least one of the x-axis, the y-axis, and thez-axis, is signaled for each of the cuboids

According to exemplary embodiments, the computer program code furtherincludes determining code configured to cause the at least one processorto determine whether a flag is set to the leaf node limiting at leastone direction along which the leaf node may not be split.

According to exemplary embodiments, the computer program code furtherincludes determining code configured to cause the at least one processorto determine the splitting pattern according to a rate-distortionoptimization (RDO) scheme

According to exemplary embodiments, splitting the leaf node into theplurality of cuboids comprises splitting the leaf node in half.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features, nature, and various advantages of the disclosedsubject matter will be more apparent from the following detaileddescription and the accompanying drawings in which:

FIGS. 1-9B are schematic illustrations of diagrams in accordance withembodiments.

FIGS. 10 and 11 are simplified block diagrams in accordance withembodiments.

FIG. 12 is a simplified illustration in accordance with embodiments.

FIG. 13 is a simplified flow illustration in accordance withembodiments.

FIG. 14 is a schematic illustration of a diagram in accordance withembodiments.

DETAILED DESCRIPTION

The proposed features discussed below may be used separately or combinedin any order. Further, the embodiments may be implemented by processingcircuitry (e.g., one or more processors or one or more integratedcircuits). In one example, the one or more processors execute a programthat is stored in a non-transitory computer-readable medium.

FIG. 1 illustrates a simplified block diagram of a communication system100 according to an embodiment of the present disclosure. Thecommunication system 100 may include at least two terminals 102 and 103interconnected via a network 105. For unidirectional transmission ofdata, a first terminal 103 may code video data at a local location fortransmission to the other terminal 102 via the network 105. The secondterminal 102 may receive the coded video data of the other terminal fromthe network 105, decode the coded data and display the recovered videodata. Unidirectional data transmission may be common in media servingapplications and the like.

FIG. 1 illustrates a second pair of terminals 101 and 104 provided tosupport bidirectional transmission of coded video that may occur, forexample, during videoconferencing. For bidirectional transmission ofdata, each terminal 101 and 104 may code video data captured at a locallocation for transmission to the other terminal via the network 105.Each terminal 101 and 104 also may receive the coded video datatransmitted by the other terminal, may decode the coded data and maydisplay the recovered video data at a local display device.

In FIG. 1, the terminals 101, 102, 103 and 104 may be illustrated asservers, personal computers and smart phones but the principles of thepresent disclosure are not so limited. Embodiments of the presentdisclosure find application with laptop computers, tablet computers,media players and/or dedicated video conferencing equipment. The network105 represents any number of networks that convey coded video data amongthe terminals 101, 102, 103 and 104, including for example wirelineand/or wireless communication networks. The communication network 105may exchange data in circuit-switched and/or packet-switched channels.Representative networks include telecommunications networks, local areanetworks, wide area networks and/or the Internet. For the purposes ofthe present discussion, the architecture and topology of the network 105may be immaterial to the operation of the present disclosure unlessexplained herein below.

FIG. 2 illustrates, as an example for an application for the disclosedsubject matter, the placement of a video encoder and decoder in astreaming environment. The disclosed subject matter can be equallyapplicable to other video enabled applications, including, for example,video conferencing, digital TV, storing of compressed video on digitalmedia including CD, DVD, memory stick and the like, and so on.

A streaming system may include a capture subsystem 203, that can includea video source 201, for example a digital camera, creating, for example,an uncompressed video sample stream 213. That sample stream 213 may beemphasized as a high data volume when compared to encoded videobitstreams and can be processed by an encoder 202 coupled to the camera201. The encoder 202 can include hardware, software, or a combinationthereof to enable or implement aspects of the disclosed subject matteras described in more detail below. The encoded video bitstream 204,which may be emphasized as a lower data volume when compared to thesample stream, can be stored on a streaming server 205 for future use.One or more streaming clients 212 and 207 can access the streamingserver 205 to retrieve copies 208 and 206 of the encoded video bitstream204. A client 212 can include a video decoder 211 which decodes theincoming copy of the encoded video bitstream 208 and creates an outgoingvideo sample stream 210 that can be rendered on a display 209 or otherrendering device (not depicted). In some streaming systems, the videobitstreams 204, 206 and 208 can be encoded according to certain videocoding/compression standards. Examples of those standards are notedabove and described further herein.

FIG. 3 may be a functional block diagram of a video decoder 300according to an embodiment of the present invention.

A receiver 302 may receive one or more codec video sequences to bedecoded by the decoder 300; in the same or another embodiment, one codedvideo sequence at a time, where the decoding of each coded videosequence is independent from other coded video sequences. The codedvideo sequence may be received from a channel 301, which may be ahardware/software link to a storage device which stores the encodedvideo data. The receiver 302 may receive the encoded video data withother data, for example, coded audio data and/or ancillary data streams,that may be forwarded to their respective using entities (not depicted).The receiver 302 may separate the coded video sequence from the otherdata. To combat network jitter, a buffer memory 303 may be coupled inbetween receiver 302 and entropy decoder/parser 304 (“parser”henceforth). When receiver 302 is receiving data from a store/forwarddevice of sufficient bandwidth and controllability, or from anisosychronous network, the buffer 303 may not be needed, or can besmall. For use on best effort packet networks such as the Internet, thebuffer 303 may be required, can be comparatively large and canadvantageously of adaptive size.

The video decoder 300 may include a parser 304 to reconstruct symbols313 from the entropy coded video sequence. Categories of those symbolsinclude information used to manage operation of the decoder 300, andpotentially information to control a rendering device such as a display312 that is not an integral part of the decoder but can be coupled toit. The control information for the rendering device(s) may be in theform of Supplementary Enhancement Information (SEI messages) or VideoUsability Information parameter set fragments (not depicted). The parser304 may parse/entropy-decode the coded video sequence received. Thecoding of the coded video sequence can be in accordance with a videocoding technology or standard, and can follow principles well known to aperson skilled in the art, including variable length coding, Huffmancoding, arithmetic coding with or without context sensitivity, and soforth. The parser 304 may extract from the coded video sequence, a setof subgroup parameters for at least one of the subgroups of pixels inthe video decoder, based upon at least one parameters corresponding tothe group. Subgroups can include Groups of Pictures (GOPs), pictures,tiles, slices, macroblocks, Coding Units (CUs), blocks, Transform Units(TUs), Prediction Units (PUs) and so forth. The entropy decoder/parsermay also extract from the coded video sequence information such astransform coefficients, quantizer parameter values, motion vectors, andso forth.

The parser 304 may perform entropy decoding/parsing operation on thevideo sequence received from the buffer 303, so to create symbols 313.The parser 304 may receive encoded data, and selectively decodeparticular symbols 313. Further, the parser 304 may determine whetherthe particular symbols 313 are to be provided to a Motion CompensationPrediction unit 306, a scaler/inverse transform unit 305, an IntraPrediction Unit 307, or a loop filter 311.

Reconstruction of the symbols 313 can involve multiple different unitsdepending on the type of the coded video picture or parts thereof (suchas: inter and intra picture, inter and intra block), and other factors.Which units are involved, and how, can be controlled by the subgroupcontrol information that was parsed from the coded video sequence by theparser 304. The flow of such subgroup control information between theparser 304 and the multiple units below is not depicted for clarity.

Beyond the functional blocks already mentioned, decoder 300 can beconceptually subdivided into a number of functional units as describedbelow. In a practical implementation operating under commercialconstraints, many of these units interact closely with each other andcan, at least partly, be integrated into each other. However, for thepurpose of describing the disclosed subject matter, the conceptualsubdivision into the functional units below is appropriate.

A first unit is the scaler/inverse transform unit 305. Thescaler/inverse transform unit 305 receives quantized transformcoefficient as well as control information, including which transform touse, block size, quantization factor, quantization scaling matrices,etc. as symbol(s) 313 from the parser 304. It can output blockscomprising sample values, that can be input into aggregator 310.

In some cases, the output samples of the scaler/inverse transform 305can pertain to an intra coded block; that is: a block that is not usingpredictive information from previously reconstructed pictures, but canuse predictive information from previously reconstructed parts of thecurrent picture. Such predictive information can be provided by an intrapicture prediction unit 307. In some cases, the intra picture predictionunit 307 generates a block of the same size and shape of the block underreconstruction, using surrounding already reconstructed informationfetched from the current (partly reconstructed) picture 309. Theaggregator 310, in some cases, adds, on a per sample basis, theprediction information the intra prediction unit 307 has generated tothe output sample information as provided by the scaler/inversetransform unit 305.

In other cases, the output samples of the scaler/inverse transform unit305 can pertain to an inter coded, and potentially motion compensatedblock. In such a case, a Motion Compensation Prediction unit 306 canaccess reference picture memory 308 to fetch samples used forprediction. After motion compensating the fetched samples in accordancewith the symbols 313 pertaining to the block, these samples can be addedby the aggregator 310 to the output of the scaler/inverse transform unit(in this case called the residual samples or residual signal) so togenerate output sample information. The addresses within the referencepicture memory form where the motion compensation unit fetchesprediction samples can be controlled by motion vectors, available to themotion compensation unit in the form of symbols 313 that can have, forexample X, Y, and reference picture components. Motion compensation alsocan include interpolation of sample values as fetched from the referencepicture memory when sub-sample exact motion vectors are in use, motionvector prediction mechanisms, and so forth.

The output samples of the aggregator 310 can be subject to various loopfiltering techniques in the loop filter unit 311. Video compressiontechnologies can include in-loop filter technologies that are controlledby parameters included in the coded video bitstream and made availableto the loop filter unit 311 as symbols 313 from the parser 304, but canalso be responsive to meta-information obtained during the decoding ofprevious (in decoding order) parts of the coded picture or coded videosequence, as well as responsive to previously reconstructed andloop-filtered sample values.

The output of the loop filter unit 311 can be a sample stream that canbe output to the render device 312 as well as stored in the referencepicture memory 557 for use in future inter-picture prediction.

Certain coded pictures, once fully reconstructed, can be used asreference pictures for future prediction. Once a coded picture is fullyreconstructed and the coded picture has been identified as a referencepicture (by, for example, parser 304), the current reference picture 309can become part of the reference picture buffer 308, and a fresh currentpicture memory can be reallocated before commencing the reconstructionof the following coded picture.

The video decoder 300 may perform decoding operations according to apredetermined video compression technology that may be documented in astandard, such as ITU-T Rec. H.265. The coded video sequence may conformto a syntax specified by the video compression technology or standardbeing used, in the sense that it adheres to the syntax of the videocompression technology or standard, as specified in the videocompression technology document or standard and specifically in theprofiles document therein. Also necessary for compliance can be that thecomplexity of the coded video sequence is within bounds as defined bythe level of the video compression technology or standard. In somecases, levels restrict the maximum picture size, maximum frame rate,maximum reconstruction sample rate (measured in, for example megasamplesper second), maximum reference picture size, and so on. Limits set bylevels can, in some cases, be further restricted through HypotheticalReference Decoder (HRD) specifications and metadata for HRD buffermanagement signaled in the coded video sequence.

In an embodiment, the receiver 302 may receive additional (redundant)data with the encoded video. The additional data may be included as partof the coded video sequence(s). The additional data may be used by thevideo decoder 300 to properly decode the data and/or to more accuratelyreconstruct the original video data. Additional data can be in the formof, for example, temporal, spatial, or signal-to-noise ratio (SNR)enhancement layers, redundant slices, redundant pictures, forward errorcorrection codes, and so on.

FIG. 4 may be a functional block diagram of a video encoder 400according to an embodiment of the present disclosure.

The encoder 400 may receive video samples from a video source 401 (thatis not part of the encoder) that may capture video image(s) to be codedby the encoder 400.

The video source 401 may provide the source video sequence to be codedby the encoder (303) in the form of a digital video sample stream thatcan be of any suitable bit depth (for example: 8 bit, 10 bit, 12 bit, .. . ), any colorspace (for example, BT.601 Y CrCB, RGB, . . . ) and anysuitable sampling structure (for example Y CrCb 4:2:0, Y CrCb 4:4:4). Ina media serving system, the video source 401 may be a storage devicestoring previously prepared video. In a videoconferencing system, thevideo source 401 may be a camera that captures local image informationas a video sequence. Video data may be provided as a plurality ofindividual pictures that impart motion when viewed in sequence. Thepictures themselves may be organized as a spatial array of pixels,wherein each pixel can comprise one or more samples depending on thesampling structure, color space, etc. in use. A person skilled in theart can readily understand the relationship between pixels and samples.The description below focuses on samples.

According to an embodiment, the encoder 400 may code and compress thepictures of the source video sequence into a coded video sequence 410 inreal time or under any other time constraints as required by theapplication. Enforcing appropriate coding speed is one function ofController 402. Controller controls other functional units as describedbelow and is functionally coupled to these units. The coupling is notdepicted for clarity. Parameters set by controller can include ratecontrol related parameters (picture skip, quantizer, lambda value ofrate-distortion optimization techniques, . . . ), picture size, group ofpictures (GOP) layout, maximum motion vector search range, and so forth.A person skilled in the art can readily identify other functions ofcontroller 402 as they may pertain to video encoder 400 optimized for acertain system design.

Some video encoders operate in what a person skilled in the art readilyrecognizes as a “coding loop.” As an oversimplified description, acoding loop can consist of the encoding part of an encoder 402 (“sourcecoder” henceforth) (responsible for creating symbols based on an inputpicture to be coded, and a reference picture(s)), and a (local) decoder406 embedded in the encoder 400 that reconstructs the symbols to createthe sample data that a (remote) decoder also would create (as anycompression between symbols and coded video bitstream is lossless in thevideo compression technologies considered in the disclosed subjectmatter). That reconstructed sample stream is input to the referencepicture memory 405. As the decoding of a symbol stream leads tobit-exact results independent of decoder location (local or remote), thereference picture buffer content is also bit exact between local encoderand remote encoder. In other words, the prediction part of an encoder“sees” as reference picture samples exactly the same sample values as adecoder would “see” when using prediction during decoding. Thisfundamental principle of reference picture synchronicity (and resultingdrift, if synchronicity cannot be maintained, for example because ofchannel errors) is well known to a person skilled in the art.

The operation of the “local” decoder 406 can be the same as of a“remote” decoder 300, which has already been described in detail abovein conjunction with FIG. 3. Briefly referring also to FIG. 4, however,as symbols are available and en/decoding of symbols to a coded videosequence by entropy coder 408 and parser 304 can be lossless, theentropy decoding parts of decoder 300, including channel 301, receiver302, buffer 303, and parser 304 may not be fully implemented in localdecoder 406.

An observation that can be made at this point is that any decodertechnology except the parsing/entropy decoding that is present in adecoder also necessarily needs to be present, in substantially identicalfunctional form, in a corresponding encoder. The description of encodertechnologies can be abbreviated as they are the inverse of thecomprehensively described decoder technologies. Only in certain areas amore detail description is required and provided below.

As part of its operation, the source coder 403 may perform motioncompensated predictive coding, which codes an input frame predictivelywith reference to one or more previously-coded frames from the videosequence that were designated as “reference frames.” In this manner, thecoding engine 407 codes differences between pixel blocks of an inputframe and pixel blocks of reference frame(s) that may be selected asprediction reference(s) to the input frame.

The local video decoder 406 may decode coded video data of frames thatmay be designated as reference frames, based on symbols created by thesource coder 403. Operations of the coding engine 407 may advantageouslybe lossy processes. When the coded video data may be decoded at a videodecoder (not shown in FIG. 4), the reconstructed video sequencetypically may be a replica of the source video sequence with someerrors. The local video decoder 406 replicates decoding processes thatmay be performed by the video decoder on reference frames and may causereconstructed reference frames to be stored in the reference picturecache 405. In this manner, the encoder 400 may store copies ofreconstructed reference frames locally that have common content as thereconstructed reference frames that will be obtained by a far-end videodecoder (absent transmission errors).

The predictor 404 may perform prediction searches for the coding engine407. That is, for a new frame to be coded, the predictor 404 may searchthe reference picture memory 405 for sample data (as candidate referencepixel blocks) or certain metadata such as reference picture motionvectors, block shapes, and so on, that may serve as an appropriateprediction reference for the new pictures. The predictor 404 may operateon a sample block-by-pixel block basis to find appropriate predictionreferences. In some cases, as determined by search results obtained bythe predictor 404, an input picture may have prediction references drawnfrom multiple reference pictures stored in the reference picture memory405.

The controller 402 may manage coding operations of the video coder 403,including, for example, setting of parameters and subgroup parametersused for encoding the video data.

Output of all aforementioned functional units may be subjected toentropy coding in the entropy coder 408. The entropy coder translatesthe symbols as generated by the various functional units into a codedvideo sequence, by loss-less compressing the symbols according totechnologies known to a person skilled in the art as, for exampleHuffman coding, variable length coding, arithmetic coding, and so forth.

The transmitter 409 may buffer the coded video sequence(s) as created bythe entropy coder 408 to prepare it for transmission via a communicationchannel 411, which may be a hardware/software link to a storage devicewhich would store the encoded video data. The transmitter 409 may mergecoded video data from the video coder 403 with other data to betransmitted, for example, coded audio data and/or ancillary data streams(sources not shown).

The controller 402 may manage operation of the encoder 400. Duringcoding, the controller 405 may assign to each coded picture a certaincoded picture type, which may affect the coding techniques that may beapplied to the respective picture. For example, pictures often may beassigned as one of the following frame types:

An Intra Picture (I picture) may be one that may be coded and decodedwithout using any other frame in the sequence as a source of prediction.Some video codecs allow for different types of Intra pictures,including, for example Independent Decoder Refresh Pictures. A personskilled in the art is aware of those variants of I pictures and theirrespective applications and features.

A Predictive picture (P picture) may be one that may be coded anddecoded using intra prediction or inter prediction using at most onemotion vector and reference index to predict the sample values of eachblock.

A Bi-directionally Predictive Picture (B Picture) may be one that may becoded and decoded using intra prediction or inter prediction using atmost two motion vectors and reference indices to predict the samplevalues of each block. Similarly, multiple-predictive pictures can usemore than two reference pictures and associated metadata for thereconstruction of a single block.

Source pictures commonly may be subdivided spatially into a plurality ofsample blocks (for example, blocks of 4×4, 8×8, 4×8, or 16×16 sampleseach) and coded on a block-by-block basis. Blocks may be codedpredictively with reference to other (already coded) blocks asdetermined by the coding assignment applied to the blocks' respectivepictures. For example, blocks of I pictures may be codednon-predictively or they may be coded predictively with reference toalready coded blocks of the same picture (spatial prediction or intraprediction). Pixel blocks of P pictures may be coded non-predictively,via spatial prediction or via temporal prediction with reference to onepreviously coded reference pictures. Blocks of B pictures may be codednon-predictively, via spatial prediction or via temporal prediction withreference to one or two previously coded reference pictures.

The video coder 400 may perform coding operations according to apredetermined video coding technology or standard, such as ITU-T Rec.H.265. In its operation, the video coder 400 may perform variouscompression operations, including predictive coding operations thatexploit temporal and spatial redundancies in the input video sequence.The coded video data, therefore, may conform to a syntax specified bythe video coding technology or standard being used.

In an embodiment, the transmitter 409 may transmit additional data withthe encoded video. The source coder 403 may include such data as part ofthe coded video sequence. Additional data may comprisetemporal/spatial/SNR enhancement layers, other forms of redundant datasuch as redundant pictures and slices, Supplementary EnhancementInformation (SEI) messages, Visual Usability Information (VUI) parameterset fragments, and so on.

FIG. 5 illustrates intra prediction modes used in HEVC and JEM. Tocapture the arbitrary edge directions presented in natural video, thenumber of directional intra modes is extended from 33, as used in HEVC,to 65. The additional directional modes in JEM on top of HEVC aredepicted as dotted arrows in FIG. 1 (b), and the planar and DC modesremain the same. These denser directional intra prediction modes applyfor all block sizes and for both luma and chroma intra predictions. Asshown in FIG. 5, the directional intra prediction modes as identified bydotted arrows, which is associated with an odd intra prediction modeindex, are called odd intra prediction modes. The directional intraprediction modes as identified by solid arrows, which are associatedwith an even intra prediction mode index, are called even intraprediction modes. In this document, the directional intra predictionmodes, as indicated by solid or dotted arrows in FIG. 5 are alsoreferred as angular modes.

In JEM, a total of 67 intra prediction modes are used for luma intraprediction. To code an intra mode, an most probable mode (MPM) list ofsize 6 is built based on the intra modes of the neighboring blocks. Ifintra mode is not from the MPM list, a flag is signaled to indicatewhether intra mode belongs to the selected modes. In JEM-3.0, there are16 selected modes, which are chosen uniformly as every fourth angularmode. In JVET-D0114 and JVET-G0060, 16 secondary MPMs are derived toreplace the uniformly selected modes.

FIG. 6 illustrates N reference tiers exploited for intra directionalmodes. There is a block unit 611, a segment A 601, a segment B 602, asegment C 603, a segment D 604, a segment E 605, a segment F 606, afirst reference tier 610, a second reference tier 609, a third referencetier 608 and a fourth reference tier 607.

In both HEVC and JEM, as well as some other standards such as H.264/AVC,the reference samples used for predicting the current block arerestricted to a nearest reference line (row or column). In the method ofmultiple reference line intra prediction, the number of candidatereference lines (row or columns) are increased from one (i.e. thenearest) to N for the intra directional modes, where N is an integergreater than or equal to one. FIG. 2 takes 4×4 prediction unit (PU) asan example to show the concept of the multiple line intra directionalprediction method. An intra-directional mode could arbitrarily chooseone of N reference tiers to generate the predictors. In other words, thepredictor p(x,y) is generated from one of the reference samples S1, S2,. . . , and SN. A flag is signaled to indicate which reference tier ischosen for an intra-directional mode. If N is set as 1, the intradirectional prediction method is the same as the traditional method inJEM 2.0. In FIG. 6, the reference lines 610, 609, 608 and 607 arecomposed of six segments 601, 602, 603, 604, 605 and 606 together withthe top-left reference sample. In this document, a reference tier isalso called a reference line. The coordinate of the top-left pixelwithin current block unit is (0,0) and the top left pixel in the 1streference line is (−1,−1).

In JEM, for the luma component, the neighboring samples used for intraprediction sample generations are filtered before the generationprocess. The filtering is controlled by the given intra prediction modeand transform block size. If the intra prediction mode is DC or thetransform block size is equal to 4×4, neighboring samples are notfiltered. If the distance between the given intra prediction mode andvertical mode (or horizontal mode) is larger than predefined threshold,the filtering process is enabled. For neighboring sample filtering, [1,2, 1] filter and bi-linear filters are used.

A position dependent intra prediction combination (PDPC) method is anintra prediction method which invokes a combination of the un-filteredboundary reference samples and HEVC style intra prediction with filteredboundary reference samples. Each prediction sample pred[x][y] located at(x, y) is calculated as follows:

pred[x][y]=(wL*R _(−1,y) +wT*R _(x,−1) +wTL*R_(−1,−1)+(64−wL−wT−wTL)*pred[x][y]+32)>>6   (Eq. 2-1)

where R_(x,−1), R_(−1,y) represent the unfiltered reference sampleslocated at top and left of current sample (x, y), respectively, andR_(−1,−1) represents the unfiltered reference sample located at thetop-left corner of the current block. The weightings are calculated asbelow,

wT=32>>((y<<1)>>shift)  (Eq. 2-2)

wL=32>>((x<<1)>>shift)  (Eq. 2-3)

wTL=−(wL>>4)−(wT>>4)  (Eq. 2-4)

shift=(log 2(width)+log 2(height)+2)>>2  (Eq. 2-5).

FIG. 7 illustrates a diagram 700 in which DC mode PDPC weights (wL, wT,wTL) for (0, 0) and (1, 0) positions inside one 4×4 block. If PDPC isapplied to DC, planar, horizontal, and vertical intra modes, additionalboundary filters are not needed, such as the HEVC DC mode boundaryfilter or horizontal/vertical mode edge filters. FIG. 7 illustrates thedefinition of reference samples Rx, −1, R−1, y and R−1,−1 for PDPCapplied to the top-right diagonal mode. The prediction sample pred(x′,y′) is located at (x′, y′) within the prediction block. The coordinate xof the reference sample Rx, −1 is given by: x=x′+y′+1, and thecoordinate y of the reference sample R−1, y is similarly given by:y=x′+y′+1.

FIG. 8 illustrates a Local Illumination Compensation (LIC) diagram 800and is based on a linear model for illumination changes, using a scalingfactor a and an offset b. And it is enabled or disabled adaptively foreach inter-mode coded coding unit (CU).

When LIC applies for a CU, a least square error method is employed toderive the parameters a and b by using the neighboring samples of thecurrent CU and their corresponding reference samples. More specifically,as illustrated in FIG. 8, the subsampled (2:1 subsampling) neighboringsamples of the CU and the corresponding samples (identified by motioninformation of the current CU or sub-CU) in the reference picture areused. The IC parameters are derived and applied for each predictiondirection separately.

When a CU is coded with merge mode, the LIC flag is copied fromneighboring blocks, in a way similar to motion information copy in mergemode; otherwise, an LIC flag is signaled for the CU to indicate whetherLIC applies or not.

FIG. 9A illustrates intra prediction modes 900 used in HEVC. In HEVC,there are total 35 intra prediction modes, among which mode 10 ishorizontal mode, mode 26 is vertical mode, and mode 2, mode 18 and mode34 are diagonal modes. The intra prediction modes are signaled by threemost probable modes (MPMs) and 32 remaining modes.

FIG. 9B illustrates, in embodiments of VVC, there are total 87 intraprediction modes where mode 18 is horizontal mode, mode 50 is verticalmode, and mode 2, mode 34 and mode 66 are diagonal modes. Modes −1˜-10and Modes 67˜76 are called Wide-Angle Intra Prediction (WAIP) modes.

The prediction sample pred(x,y) located at position (x, y) is predictedusing an intra prediction mode (DC, planar, angular) and a linearcombination of reference samples according to the PDPC expression:

pred(x,y)=(wL×R−1,y+wT×Rx,−1−wTL×R−1,−1+(64−wL−wT+wTL)×pred(x,y)+32)>>6

where Rx, −1, R−1, y represent the reference samples located at the topand left of current sample (x, y), respectively, and R−1, −1 representsthe reference sample located at the top-left corner of the currentblock.

For the DC mode the weights are calculated as follows for a block withdimensions width and height:

wT=32>>((y<<1)>>nScale),wL=32>>((x<<1)>>nScale),wTL=(wL>>4)+(wT>>4),

with nScale=(log 2(width)−2+log 2(height)−2+2)>>2, where wT denotes theweighting factor for the reference sample located in the above referenceline with the same horizontal coordinate, wL denotes the weightingfactor for the reference sample located in the left reference line withthe same vertical coordinate, and wTL denotes the weighting factor forthe top-left reference sample of the current block, nScale specifies howfast weighting factors decrease along the axis (wL decreasing from leftto right or wT decreasing from top to bottom), namely weighting factordecrement rate, and it is the same along x-axis (from left to right) andy-axis (from top to bottom) in current design. And 32 denotes theinitial weighting factors for the neighboring samples, and the initialweighting factor is also the top (left or top-left) weightings assignedto top-left sample in current CB, and the weighting factors ofneighboring samples in PDPC process should be equal to or less than thisinitial weighting factor.

For planar mode wTL=0, while for horizontal mode wTL=wT and for verticalmode wTL=wL. The PDPC weights can be calculated with adds and shiftsonly. The value of pred(x,y) can be computed in a single step using Eq.1.

FIGS. 10 and 11 are simplified block diagrams 1000 and 1100 respectivelyin accordance with embodiments and provide a different overview of ageometry based point cloud compression (G-PCC) encoder and decoder. Inboth the encoder and decoder, point cloud positions are coded first.Attribute coding depends on the decoded geometry. In FIGS. 10 and 11,region adaptive hierarchical transform (RAHT) and surface approximationmodules are options typically used for Category 1 data. Generate levelof detail (LOD) and lifting modules are options typically used forCategory 3 data. All the other modules are common between Categories 1and 3.

For Category 3 data, the compressed geometry may be represented as anoctree from the root all the way down to a leaf level of individualvoxels. For Category 1 data, the compressed geometry may be representedby a pruned octree (i.e., an octree from the root down to a leaf levelof blocks larger than voxels) plus a model that approximates the surfacewithin each leaf of the pruned octree. In this way, both Category 1 and3 data share the octree coding mechanism, while Category 1 data may inaddition approximate the voxels within each leaf with a surface model.The surface model used is a triangulation comprising 1-10 triangles perblock, resulting in a triangle soup. The Category 1 geometry codec istherefore known as the Trisoup geometry codec, while the Category 3geometry codec is known as the Octree geometry codec.

There are three attribute coding methods in G-PCC: RAHT coding,interpolation-based hierarchical nearest-neighbor prediction (PredictingTransform), and interpolation-based hierarchical nearest-neighborprediction with an update/lifting step (Lifting Transform). RAHT andLifting are typically used for Category 1 data, while Predicting istypically used for Category 3 data. However, either method may be usedfor any data, and, just like with the geometry codecs in G-PCC, the userhas the option to choose which of the 3 attribute codecs they would liketo use.

According to exemplary embodiments, the geometry may be first codedlosslessly up to a user-specified level using octree coding. Finergeometry details may then be then approximated in a lossy manner using aset (a.k.a soup) of triangles. A separate set of triangles may bederived at each leaf node of the octree that collectively approximate asurface (manifold) passing through the corresponding cube. To create thesoup, a single vertex may be derived for each edge of the cube whichimplies that we have at most 12 vertices at our disposal to approximatethe surface. Smooth surfaces can be modeled sufficiently well using the12 available free parameters; however, it may happen that the manifoldis too complicated to model using this limited number of freeparameters. As such, exemplary embodiments generalize the Trisouptechnology adopted in the MPEG/G-PCC to tackle this problem, and arate-distortion optimization (RDO) scheme is also anticipated for theproposed generalized Trisoup.

The proposed methods may be used separately or combined in any order.Further, each of the methods (or embodiments), encoder, and decoder maybe implemented by processing circuitry (e.g., one or more processors orone or more integrated circuits). In one example, the one or moreprocessors execute a program that is stored in a non-transitorycomputer-readable medium.

FIG. 12 is a simplified illustration 1200 in accordance with embodimentsand shows examples 1201 of created Trisoups at leaves. For each uniqueedge, such as exemplary edge 1202 among others shown among the examples1201, a flag may be coded indicating that whether it has a vertex, suchas the exemplary vertex 1203 among others, or not. If an edge has avertex, the location of vertex along that edge may also be coded. Eachedge may be allowed to have at most one vertex according to exemplaryembodiments.

FIG. 13 is a simplified flow illustration 1300 in accordance withembodiments and it will be understood that one or more of the featurescould be used separately from one or more other features illustratedand/or in a different order than illustrated.

According to exemplary embodiments, as S1301 there is obtained a one ormore leaf nodes, and at S1302 there is created two or more trianglesoups at each leaf node. This would be helpful to better model amanifold that is too complicated to be modeled using only one soup oftriangles. To this end, there is, at S1302 first splitting of each leafnode into two or more smaller rectangular/square cuboids. A separatetriangle soup may then be derived at S1303 for each generated cuboid.Splitting the leaf node into smaller cuboids introduces a new set ofcorner points as well as a new set of edges. For example, an edge of aleaf node could be broken in half which consequently generates one newcorner point between the end points of that edge, and also replaces theedge with two shorter new ones according to exemplary embodiments, andalso a fixed splitting pattern could be used for all the leaves and/or,as described further below, the splitting pattern could be derivedadaptively for each leaf node and signaled accordingly.

According to exemplary embodiments, as illustrated in FIG. 13, the S1302may include one or more of the steps S1304-S1310. For example, at S1306,there may be a signally of the splitting pattern of each leaf node, andaccording to embodiments, a strategy may be to signal only 2 bits perleaf node to indicate the splitting pattern:

-   -   00⇒no split (1 Trisoup)    -   01⇒split leaf node in half along x axis (2 Trisoups)    -   10⇒split leaf node in half along y axis (2 Trisoups)    -   11⇒split leaf node in half along z axis (2 Trisoups)

Such splitting pattern may be entropy coded and written at S1321 to thefinal bit stream. Various splitting patterns could be designed andadopted. If the number of adopted splitting patterns is N, [log₂ N] bitsare needed to signal the pattern per leaf node.

Also according to one or more exemplary embodiments, the triangle soupsmay be derived recursively at S1309 at each leaf node. For each cuboid,three bits, denoted by xyz, may be signaled at each split level. Forexample, at split level 0, the leaf node may be split in eight ways:

xyz=000⇒no split (1 Trisoups)

xyz=001⇒split leaf node in half along x axis (2 Trisoups)

xyz=010⇒split leaf node in half along y axis (2 Trisoups)

xyz=011⇒split leaf node in half along z axis (2 Trisoups)

xyz=100⇒split leaf node in half along x and y axis (4 Trisoups)

xyz=101⇒split leaf node in half along x and z axis (4 Trisoups)

xyz=110⇒split leaf node in half along y and z axis (4 Trisoups)

xyz=111⇒split leaf node in half along x, y, and z axis (8 Trisoups)

Likewise, at split level 1, three additional bits may be needed tosignal the splitting pattern at each cuboid generated at level 0. Thesebits may be entropy coded and written to the bit stream at S1321.

Also according to one or more exemplary embodiments, splitting inembodiments with respect to S1306 and S1309 may be done at an arbitrarylocation along a particular axis. In such case(s), for each cuboid,there may also be a signal for the splitting location per axis. At anysplitting level, if the number of voxels along a particular axis is L,[log₂ L] bits are needed to signal the splitting location along thataxis. These bits are entropy coded and written to the bit stream atS1321.

Also according to one or more exemplary embodiments, a set of splittingflags corresponding to the set of unique segments may be signaled atS1304. For example, each leaf node, or one or more thereof, may beallowed to be split only along one direction (i.e., x, y, or z), or notsplit at all according to the flags. Such examples may be readilygeneralized to arbitrary splitting patterns, along arbitrary number ofaxes, at arbitrary locations, in a recursive manner. For example, ifsplitting is allowed only at the middle of a segment, a flag is signaledfor each unique segment to indicate whether that segment is split ornot. If the flag is off, at most one vertex is signaled for that uniquesegment. If the flag in on, two vertices are signaled for that uniquesegment. Knowing the set of split and non-split segments of a leaf node,the decoder, such as at S1331, can easily derive the axis along whichthat leaf node is split and generate either 1 or, 2 or 0 Trisoups.

Also, according to one or more exemplary embodiments, at S1321, an RDO(rate-distortion optimization) scheme may be used at the encoder todetermine an optimal splitting pattern. Such encoder may take any ofmultiple strategies to find an optimal splitting choice. Exemplaryembodiments, for example, denote the set of splitting options to bechecked by the encoder by Ω. For each option ω∈Ω, the encoder derives asurface which is the union of all the triangle Trisoups generated bythat splitting option denoted by T(ω). Given T(ω), encoder can computethe distortion, D(ω), between the uncoded points and the reconstructedpoints (reconstructed points are generated using T(ω) and atriangulation step followed by an up-sampling step). The optimalsplitting option is then computed by:

$\omega^{*} = {{\min\limits_{\omega \in \Omega}{D(\omega)}} + {\lambda{R(\omega)}}}$

where R(ω) is the coding rate, and λ is the Lagrangian multiplier.Further, computing the distortion (for each splitting option) usingcommon geometry metrics could be computationally expensive. Less complexmethods may be used by the encoder at the expense of reduced codinggain. Examples may be, according to exemplary embodiments, to: computethe distortion D (ω) as the average distance of uncoded points from thesurface T(ω), use early termination to stop splitting if the number ofpoints included in a cuboid drops below a certain threshold, and/orfavor splits that generate cuboids with larger point densities.

According to exemplary embodiments, a particular splitting pattern(derived either recursively or non-recursively), among a set ofavailable splitting patterns, may be signaled for each leaf node, whereeach split divides a cuboid edge always in half, and in Table 4.3.1below, however, splits may be done at arbitrary locations as in Table4.3.2.

TABLE 4.3.1 Signaling at leaf node level: split edges always in halfDescriptor generalized_trisoup_metadata ( ) {if(generalized_trisoup_enabled_flag) { generalized_trisoup_present_flagu(1) if(generalized_trisoup_present_flag) { for (i = 0; i <num_leaf_nodes; ++i) { split_pattern[ i ] u(8) } } }

TABLE 4.3.2 Signaling at leaf node level: split edges at arbitrarylocations Descriptor generalized_trisoup_metadata ( ) {if(generalized_trisoup_enabled_flag) { generalized_trisoup_present_flagu(1) if(generalized_trisoup_present_flag) { for (i = 0; i <num_leaf_nodes; ++i) { split_pattern[ i ] u(8) split_location[ i ] u(8)} } }

TABLE 4.3.3 Signaling at unique segment level for the example mentionedin embodiment e Descriptor generalized_trisoup_metadata ( ) {if(generalized_trisoup_enabled_flag) { generalized_trisoup_present_flagu(1) if(generalized_trisoup_present_flag) { count = 0 for (i = 0; i <num_unique_segments; ++i) { split_flag[ i ] u(8) if (split_flag[ i ]) {vertex[ count++ ] // vertex 1 u(8) vertex[ count++ ] // vertex 2 } } } }

According to exemplary embodiments in view of the above tables,semantically: generalized_trisoup_present_flag indicates whether thegeneralized Trisoup is used or not, split_pattern[i] indicates a bitpattern that determines the splitting pattern of a leaf node i, and ifsplitting is done recursively, split_pattern[i] is a multiple of 3corresponding to x, y, and z axes, and/or split_location[i] indicationsthe split_location. Corresponding to each 1 in split_pattern[i], asplit_location of size [log₂ L] bits is signaled, where L denotes thenumber of voxels.

Further, at S1331, there may be a decoding process including signalingat a lead node level in which inputs to this process may be: a splittingpattern corresponding to a leaf node, and/or a split location persplitting pattern (if edges are allowed to get split at arbitrarylocations).

Whereby, if edges are only allowed to get split in half, decoder decodesthe split pattern for each leaf node and creates a separate Trisoup foreach cuboid using the decoded vertexes, and if edges are allowed to getsplit at arbitrary locations, split pattern and split locations aredecoded for each leaf node. Given the split pattern and split locations,decoder thereby creates a set of triangle soups.

Further according to exemplary embodiments, at S1331, with respect tothe unique segment flag features of S1304, there may be, according toexemplary embodiments, inputs to a process of signaling at one or moreunique segment levels as: a stream of split flags per unique segment,and/or a stream of vertices.

Whereby, for each unique segment, the decoder may decode a split flag,and if the split flag is 1, the decoder may then decodes two verticesfrom the stream of vertices, and for a leaf node, once the set of splitand non-split segments are determined, the decoder may derive the axisalong which the leaf node is split. The decoder may then either create 1or 2 Trisoups for that node or may not generate a Trisoup at all.

Accordingly, by exemplary embodiments described herein, the technicalproblems noted above may be advantageously improved upon by one or moreof these technical solutions.

The techniques described above, can be implemented as computer softwareusing computer-readable instructions and physically stored in one ormore computer-readable media or by a specifically configured one or morehardware processors. For example, FIG. 14 shows a computer system 1400suitable for implementing certain embodiments of the disclosed subjectmatter.

The computer software can be coded using any suitable machine code orcomputer language, that may be subject to assembly, compilation,linking, or like mechanisms to create code comprising instructions thatcan be executed directly, or through interpretation, micro-codeexecution, and the like, by computer central processing units (CPUs),Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers orcomponents thereof, including, for example, personal computers, tabletcomputers, servers, smartphones, gaming devices, internet of thingsdevices, and the like.

The components shown in FIG. 14 for computer system 1400 are exemplaryin nature and are not intended to suggest any limitation as to the scopeof use or functionality of the computer software implementingembodiments of the present disclosure. Neither should the configurationof components be interpreted as having any dependency or requirementrelating to any one or combination of components illustrated in theexemplary embodiment of a computer system 1400.

Computer system 1400 may include certain human interface input devices.Such a human interface input device may be responsive to input by one ormore human users through, for example, tactile input (such as:keystrokes, swipes, data glove movements), audio input (such as: voice,clapping), visual input (such as: gestures), olfactory input (notdepicted). The human interface devices can also be used to capturecertain media not necessarily directly related to conscious input by ahuman, such as audio (such as: speech, music, ambient sound), images(such as: scanned images, photographic images obtain from a still imagecamera), video (such as two-dimensional video, three-dimensional videoincluding stereoscopic video).

Input human interface devices may include one or more of (only one ofeach depicted): keyboard 1401, mouse 1402, trackpad 1403, touch screen1410, joystick 1405, microphone 1406, scanner 1408, camera 1407.

Computer system 1400 may also include certain human interface outputdevices. Such human interface output devices may be stimulating thesenses of one or more human users through, for example, tactile output,sound, light, and smell/taste. Such human interface output devices mayinclude tactile output devices (for example tactile feedback by thetouch-screen 1410, or joystick 1405, but there can also be tactilefeedback devices that do not serve as input devices), audio outputdevices (such as: speakers 1409, headphones (not depicted)), visualoutput devices (such as screens 1410 to include CRT screens, LCDscreens, plasma screens, OLED screens, each with or without touch-screeninput capability, each with or without tactile feedback capability—someof which may be capable to output two dimensional visual output or morethan three dimensional output through means such as stereographicoutput; virtual-reality glasses (not depicted), holographic displays andsmoke tanks (not depicted)), and printers (not depicted).

Computer system 1400 can also include human accessible storage devicesand their associated media such as optical media including CD/DVD ROM/RW1420 with CD/DVD 1411 or the like media, thumb-drive 1422, removablehard drive or solid state drive 1423, legacy magnetic media such as tapeand floppy disc (not depicted), specialized ROM/ASIC/PLD based devicessuch as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computerreadable media” as used in connection with the presently disclosedsubject matter does not encompass transmission media, carrier waves, orother transitory signals.

Computer system 1400 can also include interface 1499 to one or morecommunication networks 1498. Networks 1498 can for example be wireless,wireline, optical. Networks 1498 can further be local, wide-area,metropolitan, vehicular and industrial, real-time, delay-tolerant, andso on. Examples of networks 1498 include local area networks such asEthernet, wireless LANs, cellular networks to include GSM, 3G, 4G, 5G,LTE and the like, TV wireline or wireless wide area digital networks toinclude cable TV, satellite TV, and terrestrial broadcast TV, vehicularand industrial to include CANBus, and so forth. Certain networks 1498commonly require external network interface adapters that attached tocertain general-purpose data ports or peripheral buses (1450 and 1451)(such as, for example USB ports of the computer system 1400; others arecommonly integrated into the core of the computer system 1400 byattachment to a system bus as described below (for example Ethernetinterface into a PC computer system or cellular network interface into asmartphone computer system). Using any of these networks 1498, computersystem 1400 can communicate with other entities. Such communication canbe uni-directional, receive only (for example, broadcast TV),uni-directional send-only (for example CANbus to certain CANbusdevices), or bi-directional, for example to other computer systems usinglocal or wide area digital networks. Certain protocols and protocolstacks can be used on each of those networks and network interfaces asdescribed above.

Aforementioned human interface devices, human-accessible storagedevices, and network interfaces can be attached to a core 1440 of thecomputer system 1400.

The core 1440 can include one or more Central Processing Units (CPU)1441, Graphics Processing Units (GPU) 1442, a graphics adapter 1417,specialized programmable processing units in the form of FieldProgrammable Gate Areas (FPGA) 1443, hardware accelerators for certaintasks 1444, and so forth. These devices, along with Read-only memory(ROM) 1445, Random-access memory 1446, internal mass storage such asinternal non-user accessible hard drives, SSDs, and the like 1447, maybe connected through a system bus 1448. In some computer systems, thesystem bus 1448 can be accessible in the form of one or more physicalplugs to enable extensions by additional CPUs, GPU, and the like. Theperipheral devices can be attached either directly to the core's systembus 1448, or through a peripheral bus 1451. Architectures for aperipheral bus include PCI, USB, and the like.

CPUs 1441, GPUs 1442, FPGAs 1443, and accelerators 1444 can executecertain instructions that, in combination, can make up theaforementioned computer code. That computer code can be stored in ROM1445 or RAM 1446. Transitional data can be also be stored in RAM 1446,whereas permanent data can be stored for example, in the internal massstorage 1447. Fast storage and retrieval to any of the memory devicescan be enabled through the use of cache memory, that can be closelyassociated with one or more CPU 1441, GPU 1442, mass storage 1447, ROM1445, RAM 1446, and the like.

The computer readable media can have computer code thereon forperforming various computer-implemented operations. The media andcomputer code can be those specially designed and constructed for thepurposes of the present disclosure, or they can be of the kind wellknown and available to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system havingarchitecture 1400, and specifically the core 1440 can providefunctionality as a result of processor(s) (including CPUs, GPUs, FPGA,accelerators, and the like) executing software embodied in one or moretangible, computer-readable media. Such computer-readable media can bemedia associated with user-accessible mass storage as introduced above,as well as certain storage of the core 1440 that are of non-transitorynature, such as core-internal mass storage 1447 or ROM 1445. Thesoftware implementing various embodiments of the present disclosure canbe stored in such devices and executed by core 1440. A computer-readablemedium can include one or more memory devices or chips, according toparticular needs. The software can cause the core 1440 and specificallythe processors therein (including CPU, GPU, FPGA, and the like) toexecute particular processes or particular parts of particular processesdescribed herein, including defining data structures stored in RAM 1446and modifying such data structures according to the processes defined bythe software. In addition or as an alternative, the computer system canprovide functionality as a result of logic hardwired or otherwiseembodied in a circuit (for example: accelerator 1444), which can operatein place of or together with software to execute particular processes orparticular parts of particular processes described herein. Reference tosoftware can encompass logic, and vice versa, where appropriate.Reference to a computer-readable media can encompass a circuit (such asan integrated circuit (IC)) storing software for execution, a circuitembodying logic for execution, or both, where appropriate. The presentdisclosure encompasses any suitable combination of hardware andsoftware.

While this disclosure has described several exemplary embodiments, thereare alterations, permutations, and various substitute equivalents, whichfall within the scope of the disclosure. It will thus be appreciatedthat those skilled in the art will be able to devise numerous systemsand methods which, although not explicitly shown or described herein,embody the principles of the disclosure and are thus within the spiritand scope thereof

What is claimed is:
 1. A method for video coding performed by at leastone processor, the method comprising: obtaining a leaf node of geometrybased point cloud compression (G-PCC) data; deriving triangle soups forcuboids split from the leaf node; and coding a plurality of flags foredges of the cuboids, wherein at least a first one of the flagsindicates a presence of vertices, of the triangle soups, on the edges,and wherein at least a second one of the flags indicates an absence ofthe vertices from the edges.
 2. The method according to claim 1, furthercomprising: entropy coding a signaling of a splitting pattern of theleaf node by two bits, wherein the two bits indicate whether the leafnode is split into the cuboids in half along one of an x-axis, a y-axis,and a z-axis.
 3. The method according to claim 2, wherein a location, atwhich the leaf node is split and along at least one of the x-axis andthe y-axis is signaled for each of the cuboids.
 4. The method accordingto claim 1, further comprising: deriving the triangle soups recursivelyat the leaf node among a plurality of leaf nodes of the G-PCC data. 5.The method according to claim 4, further comprising: entropy coding asignaling of a splitting pattern of the leaf node by three bits, whereinthe three bits indicate whether the leaf node is split into the cuboidsin half along one of an x-axis, a y-axis, a z-axis, a combination of thex-axis and the y-axis, a combination of the x-axis and the z-axis, acombination of the y-axis and the z-axis, and a combination of thex-axis, the y-axis, and the z-axis.
 6. The method according to claim 5,wherein a location, at which the leaf node is split and along at leastone of the x-axis, the y-axis, and the z-axis, is signaled for each ofthe cuboids.
 7. The method according to claim 6, further comprising:determining whether a flag is set to the leaf node limiting at least onedirection along which the leaf node may not be split.
 8. The methodaccording to claim 1, further comprising: determining a splittingpattern according to a rate-distortion optimization (RDO) scheme
 9. Themethod according to claim 1, further comprising: splitting the leaf nodeinto the plurality of cuboids by splitting the leaf node in half. 10.The method according to claim 1, further comprising: splitting the leafnode into the plurality of cuboids by splitting the leaf node intonon-equal sized portions.
 11. An apparatus for video coding, theapparatus comprising: at least one memory configured to store computerprogram code; at least one processor configured to access the computerprogram code and operate as instructed by the computer program code, thecomputer program code including: obtaining code configured to cause theat least one processor to obtain a leaf node of geometry based pointcloud compression (G-PCC) data; deriving code configured to cause the atleast one processor to derive triangle soups for cuboids split from theleaf node; and coding code configured to cause the at least oneprocessor to code a plurality of flags for edges of the cuboids, whereinat least a first one of the flags indicates a presence of vertices, ofthe triangle soups, on the edges, and wherein at least a second one ofthe flags indicates an absence of the vertices from the edges.
 12. Theapparatus according to claim 11, wherein the coding code is furtherconfigured to cause the at least one processor to entropy code asignaling of a splitting pattern of the leaf node by two bits, whereinthe two bits indicate whether the leaf node is split into the cuboids inhalf along one of an x-axis, a y-axis, and a z-axis.
 13. The apparatusaccording to claim 12, wherein a location, at which the leaf node issplit and along at least one of the x-axis and the y-axis is signaledfor each of the cuboids.
 14. The apparatus according to claim 11,wherein the deriving code is further configured to cause the at leastone processor to derive the triangle soups recursively at the leaf nodeamong a plurality of leaf nodes of the G-PCC data.
 15. The apparatusaccording to claim 14, wherein the coding code is further configured tocause the at least one processor to entropy code a signaling of asplitting pattern of the leaf node by three bits, wherein the three bitsindicate whether the leaf node is split into the cuboids in half alongone of an x-axis, a y-axis, a z-axis, a combination of the x-axis andthe y-axis, a combination of the x-axis and the z-axis, a combination ofthe y-axis and the z-axis, and a combination of the x-axis, the y-axis,and the z-axis.
 16. The apparatus according to claim 15, wherein alocation, at which the leaf node is split and along at least one of thex-axis, the y-axis, and the z-axis, is signaled for each of the cuboids.17. The apparatus according to claim 16, wherein the computer programcode further includes determining code configured to cause the at leastone processor to determine whether a flag is set to the leaf nodelimiting at least one direction along which the leaf node may not besplit.
 18. The apparatus according to claim 11, wherein the computerprogram code further includes determining code configured to cause theat least one processor to determine a splitting pattern according to arate-distortion optimization (RDO) scheme
 19. The apparatus according toclaim 11, wherein the computer program code further includes splittingcode configured to cause the at least one processor to split the leafnode into the plurality of cuboids by splitting the leaf node in half.20. A non-transitory computer readable medium storing a programconfigured to cause a computer to: obtain a leaf node of geometry basedpoint cloud compression (G-PCC) data; derive triangle soups for each ofcuboids split from the leaf node; and code a plurality of flags foredges of the cuboids, wherein at least a first one of the flagsindicates a presence of vertices, of the triangle soups, on the edges,and wherein at least a second one the flags indicates an absence of thevertices from the edges.